Shrinkwrap ngons face
As you have learned, ngons do not subdivide or deform well, and that is the very reason they should be avoided...

Also, the quality of the deformation is directly related to the amount of subdivisions of your mesh so you need a lot more vertices and faces.

A possible solution is to create a surface made out of quads.

Delete all the faces and subdivide (W) that long edge on the left side:



Make sure that you end up with an even number of vertices for the whole object



Select all of the vertices ( A)

Press the space bar and type Grid fill (note that if you have an odd number of vertices the grid fill operation will fail)

Then play with the values for Span

to get a nice distribution for the newly created quad faces.



The mesh will deform much better now.